ReasoningAges 10-12

Symbol equation puzzles

Deduce the value of a repeated mystery symbol in a two-step arithmetic equation. Review suitability for your learners before teaching.

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Age band:Ages 7-9 Ages 10-12

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Worksheet StudioPractice pack · Ages 10-12

Symbol equation puzzles

Take your time. Show your thinking.

1. If ★ represents the same whole number each time and 2 × ★ + 11 = 27, what number does ★ stand for?
2 · 11 · 27 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 6 × ★ + 20 = 32, what number does ★ stand for?
6 · 20 · 32 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 7 × ★ + 15 = 99, what number does ★ stand for?
7 · 15 · 99 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 3 × ★ + 7 = 37, what number does ★ stand for?
3 · 7 · 37 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 4 × ★ + 7 = 39, what number does ★ stand for?
4 · 7 · 39 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 2 × ★ + 18 = 28, what number does ★ stand for?
2 · 18 · 28 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 4 × ★ + 3 = 35, what number does ★ stand for?
4 · 3 · 35 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 4 × ★ + 20 = 40, what number does ★ stand for?
4 · 20 · 40 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 5 × ★ + 19 = 74, what number does ★ stand for?
5 · 19 · 74 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 8 × ★ + 7 = 55, what number does ★ stand for?
8 · 7 · 55 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 4 × ★ + 18 = 54, what number does ★ stand for?
4 · 18 · 54 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 6 × ★ + 18 = 30, what number does ★ stand for?
6 · 18 · 30 · Symbol equation puzzles

12 questions · Seed 43 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 10-12

Symbol equation puzzles

Answers and reasoning. Review before teaching.

1. If ★ represents the same whole number each time and 2 × ★ + 11 = 27, what number does ★ stand for?
8
Subtract 11 from 27 to get 16, then divide by 2: ★ = 8.
2. If ★ represents the same whole number each time and 6 × ★ + 20 = 32, what number does ★ stand for?
2
Subtract 20 from 32 to get 12, then divide by 6: ★ = 2.
3. If ★ represents the same whole number each time and 7 × ★ + 15 = 99, what number does ★ stand for?
12
Subtract 15 from 99 to get 84, then divide by 7: ★ = 12.
4. If ★ represents the same whole number each time and 3 × ★ + 7 = 37, what number does ★ stand for?
10
Subtract 7 from 37 to get 30, then divide by 3: ★ = 10.
5. If ★ represents the same whole number each time and 4 × ★ + 7 = 39, what number does ★ stand for?
8
Subtract 7 from 39 to get 32, then divide by 4: ★ = 8.
6. If ★ represents the same whole number each time and 2 × ★ + 18 = 28, what number does ★ stand for?
5
Subtract 18 from 28 to get 10, then divide by 2: ★ = 5.
7. If ★ represents the same whole number each time and 4 × ★ + 3 = 35, what number does ★ stand for?
8
Subtract 3 from 35 to get 32, then divide by 4: ★ = 8.
8. If ★ represents the same whole number each time and 4 × ★ + 20 = 40, what number does ★ stand for?
5
Subtract 20 from 40 to get 20, then divide by 4: ★ = 5.
9. If ★ represents the same whole number each time and 5 × ★ + 19 = 74, what number does ★ stand for?
11
Subtract 19 from 74 to get 55, then divide by 5: ★ = 11.
10. If ★ represents the same whole number each time and 8 × ★ + 7 = 55, what number does ★ stand for?
6
Subtract 7 from 55 to get 48, then divide by 8: ★ = 6.
11. If ★ represents the same whole number each time and 4 × ★ + 18 = 54, what number does ★ stand for?
9
Subtract 18 from 54 to get 36, then divide by 4: ★ = 9.
12. If ★ represents the same whole number each time and 6 × ★ + 18 = 30, what number does ★ stand for?
2
Subtract 18 from 30 to get 12, then divide by 6: ★ = 2.

12 questions · Seed 43 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

Symbol equation puzzles

Take your time. Show your thinking.

1. If ★ represents the same whole number each time and 2 × ★ + 11 = 27, what number does ★ stand for?
2 · 11 · 27 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 6 × ★ + 20 = 32, what number does ★ stand for?
6 · 20 · 32 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 7 × ★ + 15 = 99, what number does ★ stand for?
7 · 15 · 99 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 3 × ★ + 7 = 37, what number does ★ stand for?
3 · 7 · 37 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 4 × ★ + 7 = 39, what number does ★ stand for?
4 · 7 · 39 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 2 × ★ + 18 = 28, what number does ★ stand for?
2 · 18 · 28 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 4 × ★ + 3 = 35, what number does ★ stand for?
4 · 3 · 35 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 4 × ★ + 20 = 40, what number does ★ stand for?
4 · 20 · 40 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 5 × ★ + 19 = 74, what number does ★ stand for?
5 · 19 · 74 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 8 × ★ + 7 = 55, what number does ★ stand for?
8 · 7 · 55 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 4 × ★ + 18 = 54, what number does ★ stand for?
4 · 18 · 54 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 6 × ★ + 18 = 30, what number does ★ stand for?
6 · 18 · 30 · Symbol equation puzzles

12 questions · Seed 43 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

Symbol equation puzzles

Answers and reasoning. Review before teaching.

1. If ★ represents the same whole number each time and 2 × ★ + 11 = 27, what number does ★ stand for?
8
Subtract 11 from 27 to get 16, then divide by 2: ★ = 8.
2. If ★ represents the same whole number each time and 6 × ★ + 20 = 32, what number does ★ stand for?
2
Subtract 20 from 32 to get 12, then divide by 6: ★ = 2.
3. If ★ represents the same whole number each time and 7 × ★ + 15 = 99, what number does ★ stand for?
12
Subtract 15 from 99 to get 84, then divide by 7: ★ = 12.
4. If ★ represents the same whole number each time and 3 × ★ + 7 = 37, what number does ★ stand for?
10
Subtract 7 from 37 to get 30, then divide by 3: ★ = 10.
5. If ★ represents the same whole number each time and 4 × ★ + 7 = 39, what number does ★ stand for?
8
Subtract 7 from 39 to get 32, then divide by 4: ★ = 8.
6. If ★ represents the same whole number each time and 2 × ★ + 18 = 28, what number does ★ stand for?
5
Subtract 18 from 28 to get 10, then divide by 2: ★ = 5.
7. If ★ represents the same whole number each time and 4 × ★ + 3 = 35, what number does ★ stand for?
8
Subtract 3 from 35 to get 32, then divide by 4: ★ = 8.
8. If ★ represents the same whole number each time and 4 × ★ + 20 = 40, what number does ★ stand for?
5
Subtract 20 from 40 to get 20, then divide by 4: ★ = 5.
9. If ★ represents the same whole number each time and 5 × ★ + 19 = 74, what number does ★ stand for?
11
Subtract 19 from 74 to get 55, then divide by 5: ★ = 11.
10. If ★ represents the same whole number each time and 8 × ★ + 7 = 55, what number does ★ stand for?
6
Subtract 7 from 55 to get 48, then divide by 8: ★ = 6.
11. If ★ represents the same whole number each time and 4 × ★ + 18 = 54, what number does ★ stand for?
9
Subtract 18 from 54 to get 36, then divide by 4: ★ = 9.
12. If ★ represents the same whole number each time and 6 × ★ + 18 = 30, what number does ★ stand for?
2
Subtract 18 from 30 to get 12, then divide by 6: ★ = 2.

12 questions · Seed 43 · Age guidance, not curriculum certification